*2.1. Geometry and Grid*

In this study, a model of the first 1.5 stages in a GE-E<sup>3</sup> engine was used as the gas turbine model for the unsteady simulation. The original turbine stage has 46 stator guide vanes, 76 rotor blades in the first stage, and 48 stator guide vanes in the next half stage [15]. For accurate prediction, the pitch angles of one stator vane and two rotor blades should be the same. This assumption can be realized using a domain scaling method [16]. In this study, the number and other parameters of the rotor blades were fixed. After applying the domain scaling method, the first and second stator vanes were magnified by 46/38 times and 48/38 times, respectively. Details regarding the vanes and blades can be found in a previous numerical study [9]. In this study, we assumed that the rotor blade initially had minor damage to the middle and top sections—on both the pressure and suction sides—to investigate the influence of various damage locations on the flow, heat transfer, and aerodynamic characteristics. The damage constituted approximately 0.5% of the volume of a normal blade. The final damage used in the simulations was the smoother post-modification damage. The computational domain consisted of two stator vanes and two rotor blades, as shown in Figure 1. Figure 1b shows the designs of the undamaged reference blade and the four blades with damage at different locations.

**Figure 1.** (**a**) Computational domain used for this study; (**b**) Damaged rotor blade after modification; Top and Mid denote the top and middle regions of the blade, respectively. PS and SS denote the pressure-side and suction-side damage, respectively.

A specialized computational fluid dynamics (CFD) tool for meshing in turbomachinery analysis, ANSYS Turbogrid [17], was adopted for the mesh generation, as shown in Figure 2. We used the blade and vane geometry of the GE-E<sup>3</sup> gas turbine engine. The simulation parameters and mesh generation process for the first stage were referred to from Choi and Ryu [9]. However, we used a di fferent length for the outlet of the second stator vane (S2). Therefore, a grid-independent test had to be conducted to find an appropriate mesh size for S2. Consequently, we simulated a total of five mesh sizes and ultimately selected a mesh size of 2.4 million for the computation. Details of the grid-independent test for the second stator vane are shown in Table 1. After the grid-independent test, the total mesh size of the computational domain was approximately 8 million, with the *y*+ value being less than 0.5 at the blade surface and less than 1 at the other walls. The variations in *y*+ at different span-wise locations on the rotor blade are shown in Figure 3.

**Figure 2.** Detailed mesh of computational domain for the 1.5-stage GE-E3 gas turbine.

**Figure 3.** Variation in *y*+ at different span-wise locations in the rotor blade.


**Table 1.** Grid-independent test.
